P(x, Y) Is a Predicate and the Universe for the Variables

question 147

True/False

P(x, y) is a predicate and the universe for the variables x and y is {1, 2, 3}. Suppose
P(1, 3), P(2, 1), P(2, 2), P(2, 3), P(3, 1), P(3, 2) are true, and P(x, y) is false otherwise. Determine whether
the following statements are true.
- $$\forall y \exists x ( x \leq y \wedge P ( x , y ) )$$